# Different Variances?

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- This topic has 30 replies, 10 voices, and was last updated 13 years ago by A.S..

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- March 23, 2007 at 4:35 pm #46510

AllthingsidiotParticipant@Allthingsidiot**Include @Allthingsidiot in your post and this person will**

be notified via email.Determine whether the following 2 types of rockets have significantly different variance at the 5% level?

Rocket A

61 readings

1.347 miles

Rocket B

3 readings

2.237 miles0March 23, 2007 at 7:39 pm #153841

ratios and dfParticipant@ratios-and-df**Include @ratios-and-df in your post and this person will**

be notified via email.look at the ratios and the degrees of freedom … you don’t even have to look up the F-values in a table, it’s so obvious :-).

0March 24, 2007 at 8:38 am #153847Is it correct to compare 63 readings and 3 readings?

Is there any logic in sample sizes?

0March 24, 2007 at 9:31 am #153848

AllthingsidiotParticipant@Allthingsidiot**Include @Allthingsidiot in your post and this person will**

be notified via email.Agree

It is 31 readings for the second rocket

Thanks for your kind observation0March 24, 2007 at 5:40 pm #153851

Jim ShelorParticipant@Jim-Shelor**Include @Jim-Shelor in your post and this person will**

be notified via email.Assuming 1.347 and 2.237 are the sigmas, yes the variances are significantly different.

If 1.347 and 2.237 are the variances, there is insufficient evidence to conclude that the variances are significantly different.0March 24, 2007 at 6:01 pm #153852Wrong – show your work.

0March 24, 2007 at 10:02 pm #153855

Jim ShelorParticipant@Jim-Shelor**Include @Jim-Shelor in your post and this person will**

be notified via email.Stan,

Problem 1.

Test for Equal Variances – Assume 1.347 and 2.237 represent variances.

95% Bonferroni confidence intervals for standard deviations

Sample N Lower StDev Upper

1 61 0.96281 1.16060 1.45520

2 31 1.15891 1.49566 2.08983

F-Test (normal distribution)

Test statistic = 0.60, p-value = 0.095

p-value > alpha, fail to reject null, insufficient evidence to conclude a difference exists.Problem 2

Test for Equal Variances – Assume 1.347 and 2.237 represent sigmas. Therefore, variances are 1.814 and 5.004 respectively.

95% Bonferroni confidence intervals for standard deviations

Sample N Lower StDev Upper

1 61 1.11732 1.34685 1.68872

2 31 1.73331 2.23696 3.12562

F-Test (normal distribution)

Test statistic = 0.36, p-value = 0.001

p-value < alpha, reject null, a significant difference exists between the variance of rocket A and rocket B.

Now show your work.0March 25, 2007 at 1:02 am #153857

ratio and f valueParticipant@ratio-and-f-value**Include @ratio-and-f-value in your post and this person will**

be notified via email.The question asks if the variances are equal. As a result one simply divides the larger variance by the smaller variance, i.e.2.237/1.347 and looks up the critical value of the F-statistics for d.f = 30 and d.f = 60. The critical ratio exceeds the calculated test statistic (you don’t even have to look that up given how close the ratio is to one). As a result you reject the null hypothesis. Remember, this is a question asked by “Allthingsidiot”. So the answer cannot be that complicated :-).

0March 25, 2007 at 3:10 am #153858

Jim ShelorParticipant@Jim-Shelor**Include @Jim-Shelor in your post and this person will**

be notified via email.ratio and f value,

Assuming 1.347 and 2.237 are the variances (the numbers are not labelled so they cound be standard deviations), the ratio 2.237/1.347 = 1.66, I do not consider than very close to 1.

Working this in Minitab, I get the opposite answer from the one you get. I fail to reject the null, there is insufficient evidence to conclude there is a difference in the variances.

Test for Equal Variances – Assume 1.347 and 2.237 represent variances.

95% Bonferroni confidence intervals for standard deviations

Sample N Lower StDev Upper

1 61 0.96281 1.16060 1.45520

2 31 1.15891 1.49566 2.08983

F-Test (normal distribution)

Test statistic = 0.60, p-value = 0.095

p-value > alpha, fail to reject null, insufficient evidence to conclude a difference exists.0March 25, 2007 at 5:29 am #153860

ratio f testParticipant@ratio-f-test**Include @ratio-f-test in your post and this person will**

be notified via email.to my knowledge the 2sample variance technique under Basic Statistics asks you for the raw data, not summary data and degrees of freedom. With 30 and 60 degrees of freedom respectively your critical F value is 1.82, i.e, higher than the calculated value. Did you look the two sided test up, i.e. split 0.05?

0March 25, 2007 at 9:57 am #153862

Mat MaccallumParticipant@Mat-Maccallum**Include @Mat-Maccallum in your post and this person will**

be notified via email.1.66 is “close to” 1 when the sample sizes are 60 and 30. you would be right if the sample sizes where larger. You can prove this by getting a large real world data set finding the Stdev then getting the ratio of stdev for alot of sample sets of size 60 and 30. The ratio will be less than 1.82 95% of the time.

0March 25, 2007 at 2:08 pm #153865

Jim ShelorParticipant@Jim-Shelor**Include @Jim-Shelor in your post and this person will**

be notified via email.The Minitab 14 test for equal variances undeer basic statistics asks for summary data consisting of sample size and variance.

It calculates using the two sided alternative.

You can see the printout in my last post.

An F-Ratio Test using Excel yields:

Inputs sample 1 – 61 samples, 1.347 variance

Inputs sample 2 – 31 samples, 2.237 variance

Test Statistic – 0.6021

2 sided 2 sample cutoff values – lower 0.5509, upper 1.9400

Test statistic is > lower and < upper.

Fail to reject the null, insufficient evidence to conclude a difference in the variances.

How about somebody else showing their work instead of simply stating the answer is obvious.0March 25, 2007 at 3:43 pm #153867What’s the disagreement? You used Minitab, I used the F table. There is no other work to show. It’s a very simple F-test …

0March 25, 2007 at 3:51 pm #153868

Jim ShelorParticipant@Jim-Shelor**Include @Jim-Shelor in your post and this person will**

be notified via email.The difference is:

Your answer is reject the null.

My answer is fail to reject the null.0March 25, 2007 at 3:55 pm #153869If you had grown up using the F table to look up the critical values prior to the advent of computer software programs, you’d also simply “know” what the cut-off points for various combinations of degrees of freedom are. One small little observation though: 60 and 30 are the degrees of freedom. The corresponding samples are 61 and 31 (as in the original post). So you may have to adjust that ratio slightly … the devil’s always in the detail, and in statistics this little attention makes the difference between someone who knows … and someone who “knows” :-).

0March 25, 2007 at 4:10 pm #153870Fail to reject the null, insufficient evidence to conclude a difference in the variances.

With 30 and 60 degrees of freedom respectively your critical F value is 1.82, i.e, higher than the calculated value.

I’ll gladly look up the calculations in Minitab and compare them with my look up (very superficial indeed, but sufficient to come to the right conclusion), but if the cut-off value is higher than the calculated value, I would assume that everyone who has had basic statistics knows that this means that you fail to reject the null hypothesis :-))))). How much more basic can it get?0March 25, 2007 at 4:14 pm #153871

AllthingsidiotParticipant@Allthingsidiot**Include @Allthingsidiot in your post and this person will**

be notified via email.Thank You for make me Laugthing??

0March 25, 2007 at 4:20 pm #153872Your grammar will never improve: “Make me laugh” … but I am getting a kick out of this too … so much confusion about the simplest of all of the hypothesis tests …

0March 25, 2007 at 4:30 pm #153874

Jim ShelorParticipant@Jim-Shelor**Include @Jim-Shelor in your post and this person will**

be notified via email.Then why did you say to reject the null in your post?

0March 25, 2007 at 4:32 pm #153873

AllthingsidiotParticipant@Allthingsidiot**Include @Allthingsidiot in your post and this person will**

be notified via email.Ratio

You0March 25, 2007 at 4:35 pm #153875

AllthingsidiotParticipant@Allthingsidiot**Include @Allthingsidiot in your post and this person will**

be notified via email.Ratio

Again thank you.

You can’t blame me because I’m “Allthingsidiot” as you have recognized.I’m glad that my “stupid” question has initiated such intelligence debate,attracting clever and smart people like you and the others,please proceed forward0March 25, 2007 at 4:41 pm #153876Jim, why did you use 60 and 30 for df?It should be 60 and 2 – learn to read please.

0March 25, 2007 at 4:43 pm #153877oops … that’s correct, fail to reject … okay the tag’s on my :-).

0March 25, 2007 at 4:44 pm #153878

Jim ShelorParticipant@Jim-Shelor**Include @Jim-Shelor in your post and this person will**

be notified via email.Because the second post from Allthingsidiot changed the sample size to 31?

It0March 25, 2007 at 4:44 pm #153879

Jim ShelorParticipant@Jim-Shelor**Include @Jim-Shelor in your post and this person will**

be notified via email.Because the second post from Allthingsidiot changed the sample size to 31?

It be0March 25, 2007 at 4:44 pm #153881

Jim ShelorParticipant@Jim-Shelor**Include @Jim-Shelor in your post and this person will**

be notified via email.Because the second post from Allthingsidiot changed the sample size to 31?

It be I all0March 25, 2007 at 4:45 pm #153882sure, and continue to dream to get a job in six sigma with your Villanova University certificate … glad I can do something to brighten your obviously very sad and delusioned life :-))))).

0March 25, 2007 at 4:46 pm #153883

Jim ShelorParticipant@Jim-Shelor**Include @Jim-Shelor in your post and this person will**

be notified via email.Sorry about the multiple posts, I do not know how I did that.

0March 25, 2007 at 4:47 pm #153880

Jim ShelorParticipant@Jim-Shelor**Include @Jim-Shelor in your post and this person will**

be notified via email.Because the second post from Allthingsidiot changed the sample size to 31?

It be I0March 25, 2007 at 7:36 pm #153891

AllthingsidiotParticipant@Allthingsidiot**Include @Allthingsidiot in your post and this person will**

be notified via email.Stan

I couldn’t expect you to ask such a ” ” question?0March 26, 2007 at 2:19 am #153914Is there any criteria for sample size while doing comparative study F 0r T test etc

Sample need not be same size?

If difference in sample size is allowed,how much?

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